Solve for $n$, $ \dfrac{2}{9n - 3} = -\dfrac{n + 1}{9n - 3} + \dfrac{5}{12n - 4} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $9n - 3$ $9n - 3$ and $12n - 4$ The common denominator is $36n - 12$ To get $36n - 12$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ \dfrac{2}{9n - 3} \times \dfrac{4}{4} = \dfrac{8}{36n - 12} $ To get $36n - 12$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ -\dfrac{n + 1}{9n - 3} \times \dfrac{4}{4} = -\dfrac{4n + 4}{36n - 12} $ To get $36n - 12$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ \dfrac{5}{12n - 4} \times \dfrac{3}{3} = \dfrac{15}{36n - 12} $ This give us: $ \dfrac{8}{36n - 12} = -\dfrac{4n + 4}{36n - 12} + \dfrac{15}{36n - 12} $ If we multiply both sides of the equation by $36n - 12$ , we get: $ 8 = -4n - 4 + 15$ $ 8 = -4n + 11$ $ -3 = -4n $ $ n = \dfrac{3}{4}$